Vibrations Fundamentals and Practice ans Maintaining the outstanding features and practical approach that led the bestselling first edition to become a standard textbook in engineering classrooms worldwide, Clarence de Silva''''s Vibration: Fundamentals and Practice, Second Edition remains a solid instructional tool for modeling, analyzing, simulating, measuring, monitoring, testing, controlling, and designing for vibration in engineering systems. It condenses the author''''s distinguished and extensive experience into an easy-to-use, highly practical text that prepares students for real problems in a variety of engineering fields.
Trang 1de Silva, Clarence W “Answers to Numerical Problems”
Vibration: Fundamentals and Practice
Clarence W de Silva
Boca Raton: CRC Press LLC, 2000
Trang 2Answers to Numerical Problems
CHAPTER 2
2.22 k eq = 3EI/l3; m eq = 33m/140
2.31 (d) 2.75 × 10–2 rad·s–1, 0.564 Yes, at 2.27 × 10–2 rad·s–1
CHAPTER 3
3.5 (c) 6.455 × 103 N·s·m–1
3.7 (d) (i) r > , (ii) r > 1.73, 1.964, 2.871, 3.77, 7.075; (e) Yes
3.12 (c) 1.0, ,
3.16 (c) 1.0, ,
3.18 (a) –0.55 ±j 1.6424
CHAPTER 4
4.1 b
4.2 c
4.3 1
4.6 0.31, –72°, 0.10, –0.29, –2.7 dB
4.14 (i) 10 samples/s; (ii) 102.4 s; (iii) 1024 complex values First and last 512 give the same values; (iv) 512; (v) 0.01 Hz; (vi) 5 Hz; (vii) 400; (viii) 4 Hz
4.20 (ii) Meaningless; (iii) 2 decades; (iv) 1/2 octave; (v) No dimensions
4.21 1–80 Hz; 4–50 Hz; 1–200 Hz; 20 Hz–20 kHz; Problem dependent
CHAPTER 5
5.8 (b) (0,7/6), unstable; (π, 5/6), unstable; (π/3, 4/3), stable
5.14 (c) ω0 = 1.0 rad·s–1, ω1 = 0.765367 rad·s–1, ω2 = 1.847759 rad·s–1; θ1 = 0.25 cosω1t + 0.75 cosω2t; θ2 = cosω1t – cosω2t
CHAPTER 6
6.12 (a) 8.0 × 1010 N·m–2; (b) Steel
CHAPTER 7
7.7 (a) 0.08
7.8 (b) 0.045
7.9 (b) 0.08
7.13 0 to 2.06 × 107 N·m–1
7.14 (b) (i) 50.6 rad·s–1, 0.1; (ii) 1.5 cm; (iii) 50.1 rad·s–1, 10.02 rad·s–1
2
1 0 , 1 0.875 3 1, , 0.3974 , ( )8 3 ,
0 8603336 l ( )Gρ
Trang 3CHAPTER 8
8.4 (b) 0.99%
8.5 (d) 0.09; (e) 6.25 × 104 N·m–1 to 25.0 × 104 N·m–1
8.11 1000 Hz
8.18 100.0 s
8.20 (a) 98.37% to 99.99%; (c) 170 Hz
8.26 144.0, 5.9%
CHAPTER 9
9.2 (b) 44.5 Mbits·s–1
9.3 –7.5 V, –14 V
9.6 31.8 kHz, 5 µs
9.16 (a) 3600 rpm, 15
9.20 1%
CHAPTER 10
10.2 Directions 1, 2, 3, or 4
10.8 (a) 2000 Hz; (b) 80 Hz; (c) 50 Hz; (d) 2000 Hz; (e) 500 Hz; (f) 40 Hz
10.11 (i) 21/3; (iii) Two; (iv) 1/2
10.15 (c) 4.6 g, 30.0 rad·s–1; (d) 0.23 cm·s–1; 653.3 rad·s–1
10.17 (c) (i) 25 Hz, 80 g; 50 Hz, 160 g; (ii) 3.2 cm, 160 g; (iii) 3.2 cm, 3.0 m·s–1; 29 g; 23 g
CHAPTER 11
11.5 (b) 20 dB/decade; (c) –20 dB/decade
11.6 (a) 0.356 Hz; (b) 0.355 Hz
11.8 0.023, 0.038
11.16 1.0 rad·s–1, 0.2
CHAPTER 12
12.6 82.0 N·cm–1, 6.1 cm
12.7 2.7 × 104 N·m–1; 286.0 N·m–1·s, 38.1 rad·s–1
12.8 3.3 × 105 N·m–1, 7.8 × 103 N·m–1·s
12.9 3.3, 0.45
12.10 Mount 1
12.11 6.9 gm at –6.6°
12.12 (b) 8.9 gm at –23°
12.13 (b) Plane 1: 42.3 gm at 107°; Plane 2: 18.8 gm at 121°
12.14 (c) (iii) 0.4 kg, 2.6 kg
12.15 15.3 gm at 53.4°
12.23 0.2
12.24 (a) 2338.6 rpm; (b) 3.376 cm; (c) 17
12.28 119.2 rad·s–1
12.29 (a) 2430 cycles·m–1, 3330 cycles·m–1; (b) 2616 to 2832 rpm; (c) 2.8 × 10–3 mm·N–1,
18.4 × 10–3 mm·N–1
12.30 3.2 kg and 1.7 × 105 N·m–1
12.31 3.33 kg, 1.184 × 105 N·m–1, 180.4 N·s·m–1, 8.26/0.074
12.32 0.1
12.34 (b) 156 rad·s–1, 2.75 kg, 1.085 × 104 N·m–1, 58.7 N·m–1·s